Nucleation of the Theophylline:Salicylic Acid 1:1 Cocrystal

The nucleation behavior of the theophylline–salicylic acid 1:1 (THP:SA) cocrystal in chloroform has been investigated and compared with the corresponding behavior of the pure compounds. Induction times have been determined at different supersaturations at 10 °C under each condition in approximately 40–80 repetition experiments in 20 mL vials. Nucleation times, extracted from the median induction times by accounting for a nucleus growth time, have been used to determine the interfacial energy and the pre-exponential factor within the classical nucleation theory. Results show that the cocrystal at equal driving force has a longer nucleation time, or to reach equal nucleation time, the cocrystal requires a higher driving force. Pure theophylline is easier to nucleate than pure salicylic acid, despite the latter having a smaller molecular size, higher solubility, and is expected to form dimers already in the solution. The cocrystal is found to have an interfacial energy in between the respective values for the pure compounds. However, the higher molecular volume of the cocrystal, taken as the volume of the 1:1 theophylline–salicylic acid assembly, leads to the highest nucleation work, which, together with a low pre-exponential factor, explains why the cocrystal is the most difficult to nucleate. The experimentally extracted pre-exponential factor of the cocrystal is very similar to that of THP, and similar trends are observed from theoretical expressions of volume-diffusion- and surface-integration-controlled nucleation, respectively.

Solid phase characterisation PXRD data were collected in reflection mode with an Empyrean diffractometer (PANalytical, Phillips) equipped with CuKα1,2 radiation (γ = 1.5406 Å) operating at 40 kV and 40 mA at room temperature. Samples were scanned between 2θ values of 5 and 40° at a step size of 0.01313° 2θ/s, 73 s per step.
Differential scanning calorimetry (DSC) was performed on a Netsch Polyma 214 DSC. Samples were analysed in a nitrogenous environment with a temperature ramp rate of 10 °C min −1 over a temperature scan range from 20 and 310 °C. Crystals were isolated from solvent with Whatman filter paper. 5-7 mg of crystals were added to concavus aluminium pans which were sealed using a crimping press and then the lid was pierced. The instrument was calibrated using samples of indium and lead.
Thermogravimetric analysis (TGA) was carried out under nitrogen using TGA instrument TA Q50 V20.13 Build 39. Samples were placed on platinum pans and heated up to 500 °C at a ramp rate of 20 °C min −1 .
For single crystal x-ray diffraction (SC-XRD) analysis cocrystal material was dissolved in chloroform to create a saturated solution. A crystal of suitable quality was obtained by slow evaporation crystallisation and analysed by SC-XRD. The unit cell parameters were consistent with that on record in the CSD. 1 For Scanning Electron microscopy (SEM), following visible nucleation of vials of all three systems; TPH:SA, THP II and SA over a variety of conditions the slurry was isolated immediately. Analysis of the solid isolated from the slurry was carried out using SEM on the Jeol CARRYSCOPE, coated in gold by a 30 second sputter to ensure a fine coating and minimise ionization. Samples isolated from the same slurries were analysed also by PXRD to identify solid forms.
The THP:SA cocrystal was successfully synthesized as shown by subsequent physical characterisation including PXRD and DSC. The THP:SA cocrystal diffractogram was identical to a previously reported powder pattern for the cocrystal entered to the Cambridge structural database (CSD) under the reference code KIGLES01 (Figure 1). The PXRD pattern of the cocrystal is distinctly different to diffractograms of pure SA and the two low-temperature forms of pure THP. 1 (Figure 2). The diffractogram patterns of the samples taken from the bulk powder following synthesis revealed peaks only corresponding to THP:SA cocrystal, proving that conversion is completed within 72 h.    The temperature corresponding to the onset of each endotherm peak is labelled.
The DSC curve in Figure 4 shows the melting point of the cocrystal is between that of the API and coformer. The melting point of THP:SA is 186.2 °C, SA is 158.8 °C and THP II is 272.0 °C. A DSC curve previously reported in the literature of THP:SA shows the onset of melting as 188.5 °C 1 .
One main difference between the experiments is the different heating rates used as the work reported previously operated at 5 °C min -1 whereas the data in the current work was collected at 10 °C min -1 , sample mass also effects detection of melting peaks along with different instruments. The same cocrystal sample for which we ran DSC was also analysed by PXRD and matched the PXRD pattern reported by the authors of the previous work outlined above 1 .
The THP form II melting point is 273 °C which matches the data from the same paper. The same previous work also reports a melting point onset for SA of 159 °C, PXRD patterns supported this identification of the SA samples. The cocrystal is in the form of needles ( Fig. 5(a)), SA is also in the form of needles ( Fig. 5 (b)) and THP II is plate-like (Fig. 5(c) and (d)).
For a spherical nucleus of critical size, the nucleation free energy (ΔGcrit) per mole of nuclei (J mol -1 ), also called the nucleation work, in ESI Eq [1] is given as In Figure 5 it is shown that the nucleation work, ΔGcrit, is the highest for THP:SA closely followed by that of SA. The nucleation work is much lower for THP II. However, notably at higher supersaturation the nucleation work is even less than the kinetic energy of the system: 3/2RT and should proceed spontaneously. However, it doesn't showing one of the known weaknesses of the CNT. From ESI Eq [2] the number of molecules per critical nucleus can be estimated 2 : Where rcrit is critical radius (m), vo is molecular volume (m 3 ) as shown in Table 4 (main text), γ is interfacial energy (J m -2 ) and NA is Avogadro's number and Ncrit is the number of molecules per critical nucleus. At comparable driving force the THP:SA critical nucleus has a larger radius than SA and THP has the smallest rcrit. THP:SA requires a slightly lower number of molecules than SA to make up the nucleus. As seen in Figure 6 at comparable driving force, 724 J mol -1 (S=1.36), the least number of molecules to form a nucleus is required for the THP system (1 molecule), SA requires 15 molecules and the most required by THP:SA (16 THP:SA heterodimers which includes 16 THP and 16 SA molecules).    Table 3 presents estimation of preexponential factors using an approach where the diffusivity of the cocrystal is taken as the geometric mean of THP and SA diffusivities 3 : = √ .
[4] In this case it would be assumed that there are cocrystal assemblies diffusing throughout the liquid and therefore the Ce term used in this calculation would be the concentration of the cocrystal in equilibrium with the solid cocrystal phase and the value of vo used would be the molecular volume of the cocrystal.

Methods for calculating J
Below are 4 variations of methods used to calculate the nucleation parameters A, and γ form the nucleation rate parameter J. Method 1 is the same as what is presented in the main body of work and the others are for comparison.

Method 2 5 :
Where τ, τg and J are estimated from the best fit of the Poisson distribution to the experimental distribution.

Method 3:
Where τ, and J are estimated from the best fit of the Poisson distribution to the experimental distribution but τg is defined as the first point.

Method 4:
= 1 τ 50 Where no growth time is accounted for and J is estimated from the experimental induction times τ50.
The values of the parameters used for each method are presented in Table 5 -8.   The comparison reveals that in the SA system the Poisson distribution overestimates τ50 which, when accompanied by small τg values, results in lower than expected J values with respect to J estimated from the experimental τ50 values when a growth time is not considered. This led to a lower pre-exponential factor for SA by the method using Poisson distributions than expected. The same effect was not seen for THP:SA or THP as the Poisson distribution is a better fit to those experimental data. As the Poisson distribution does not represent the experimental data well in the SA system, the nucleation rates (J) have been estimated from the inverse of τnuc and V (eq. 6). This method was also utilised in the other systems for consistency. At the same driving force THP:SA has the lowest nucleation rate followed by SA and then THP which has the highest nucleation rate.